Skip the museums and do the architecture boat tour. It's outside, everyone loves it ( check the weather though ) it eats up a decent chunk of time without being boring, and there's a bar on the boat. Under 21's welcome.

I think Jazz Showcase (at dearborn station) allows under 21's to the early show, but it's not free. Usually tickets are like 20 bucks ish?

Assuming you've got boots already (great first purchase), if you've got some money to burn I'd highly recommend Kastle. I rented a set of the MX88's (or equivalent) in 2011 and loved them. They're light, but responsive, and for a 6'1 200lb'er had enough stiffness to really rip without sacrificing float in the soft snow. Ended up getting a set of the BMX's but can't recommend the brand enough!

edit: I ski the 188's. The longer the ski, the faster they are, but sacrifice some nimbleness.